Cheap car insurance deals are disappearing, pushing up the cost of motoring for millions of drivers. Figures due to be released by the AA this week are expected to show that people who shop around to get the cheapest cover have seen premiums rise by almost 10pc over the past year.

These increases follow a 30pc rise in premiums last year, and a similar 30pc rise the year before.

The price rises affect both comprehensive and third-party cover, but it is the insurers that offer the lowest-priced deals that are pushing up prices the most.

The AA's "shoparound" survey, which looks at the five cheapest insurance quotes across a range of different risks, is expected to show that these prices have risen by 8.5pc year on year. In contrast, the average cost of car insurance is expected to show more modest rises, closer to 4pc over the past 12 months.

Ian Crowder of the AA said this seemed to indicate that those insurers offering rock-bottom prices were getting their fingers burnt, and paying out more on claims than they were collecting on premiums.

The insurers that tend to offer the cheapest quotes on price comparison websites are often internet-only companies, rather than the larger well-known brands. But the fact that these insurers are pushing prices up has had a knock-on effect on many of the larger providers, which are now also edging prices up to improve their profit margins.

Not surprisingly, this increase has led many drivers to look at more innovative ways to cut car insurance costs. Research from the British Insurers Brokers' Association (Biba) shows that over the past two years there has been a fivefold increase in the number of people installing "black box" technology in their vehicles. These devices monitor their driving habits in a bid to cut insurance costs.

Almost 200,000 drivers have now signed up to "telematic" insurance, in some cases halving their premiums. A Biba spokesman said it expected numbers to "snowball", with more than half a million motorists opting to install the technology in exchange for lower car insurance premiums.

While this is a relatively small proportion of drivers – there are 35.5 million private cars on the road – experts predict that take-up will climb steeply over the next decade.

Take-up is already strong in the commercial fleet market and in the United States, which has pioneered the technology – around 80pc of US vehicles have these black boxes fitted as standard.

Over the next few years, demand in Britain is expected to come from female drivers and younger motorists in particular, who are likely to be disadvantaged by new European rules that come into effect at the end of this year.

The new EU directive stipulates that insurance companies will no longer be able to use a person's sex when setting premiums. The rule is likely to cause huge increases in insurance costs for many women, with those aged less than 25 facing the biggest price rises. This is because younger male drivers make the most car insurance claims – and, more importantly, make the most expensive claims, as they are more likely to be involved in a high-speed accident, causing serious injury and extensive damage to vehicles.

Currently, the average motor insurance premium is close to £3,000 for a young male driver, but just under £1,700 for women drivers of the same age. However, insurance experts said that when these new rules came into effect, women could expect to see the price they pay rise by at least 25pc, adding more than £400 to their motoring costs.

However, those who opt for black box technology will have their insurance premiums based on their actual driving record. This is likely to benefit women, as well as more cautious male drivers, who now won't be penalised simply because an insurer sees their age and sex and assumes they must be a "boy racer".

As demand for this type of insurance increases, it is expected that many more insurance companies will offer these policies. Currently the AA and Co-operative Insurance offer these deals, and Direct Line and Aviva are both expected to launch their own versions imminently, which are likely to be backed by high-profile advertising campaigns.

Mr Crowder said: "This technology is gender-neutral and those with good driving habits can expect to see premiums cut significantly."

He said that on premiums of £2,400-plus it was not uncommon to earn discounts of £600 or more for drivers who stuck to speed limits, clocked up low mileage and didn't drive too often at night. Rather than wait for a year, this money is often credited straight back to your bank account on a monthly basis – which is particularly good news for parents who cover the cost of car insurance for their offspring.

Mr Crowder said it wasn't just younger drivers who could benefit – although they were likely to see the biggest reductions in cost, as they start off with the most expensive insurance. As stated, many women will benefit – although the difference between male and female premiums narrows as people age. He added that for middle-aged drivers, who typically have safer driving records, a conventional insurance policy could be cheaper initially.

But those who have lost their no-claims discount would see a marked benefit. This is because the black box technology should allow them to earn a discount on their premium after a couple of months, rather than waiting several years to build up a substantial no-claims bonus again.

Similarly, retired drivers who believe they are still safe on the roads can benefit. Insurers often start to bump premiums up again for motorists in their seventies and eighties, as they are concerned about the higher accident rate among this age group.

It goes without saying that not all drivers who install such technology will see premiums fall. Those who have poorer driving records, who have a higher than expected mileage or who frequently drive at night could see premiums rise sharply, with the insurer often taking additional payments before the renewal date.

However, a spokesman for Biba said installing this technology could have a positive effect on people's driving habits. Likewise, many parents not only like the idea of cutting the cost of their children's car insurance but hope that a computer on the dashboard monitoring their habits may discourage them from speeding or taking other needless risks.

Some insurers offering these policies will also offer discounted places on advanced driving courses. This can help policyholders reduce premiums, as well as potentially cutting claims costs for insurers.

So what exactly do these black boxes monitor? In recent years they have become far more sophisticated, and don't simply log mileage and the time of day the car is driven. Drivers installing this technology will have access to an online record of their driving habits. This will include a speed analysis, where and when they drive and how they anticipate traffic (such as whether they hit the brakes too hard, too often), as well as how they drive around corners and adapt their driving to the circumstances.

Policyholders can access this information on a computer, or even have it downloaded via a smartphone app. This will enable them to see how they are rated in each of these categories, and if their "performance" starts to slip – potentially leading to premium increases – drivers should be notified, giving them the opportunity to improve their driving records.

Many insurers will install the technology free of charge, although they recoup the cost through their premiums. Others ask for an upfront fee. Customers are free to switch insurers if they find that they are not saving money, but there may be a charge – which can be as much as £100 – to remove the box at a later date.

In the past, take-up of the black boxes has been slow. Many drivers may be concerned about how the information is used, but there are strict data protection laws. By signing up to one of these schemes, you have given the insurer permission to use the information to set your insurance premiums, but the insurer would not be able to pass on information to third parties – for example informing the authorities that you had broken the speed limit.

Mr Crowder added: "Over the past five years, many people have become far less concerned about this type of 'Big Brother' technology. Anyone with a smartphone can now be tracked to the nearest metre, most high streets are covered by CCTV and retailers store a wealth of data on our shopping habits thanks to credit and loyalty cards. Many younger people are happy to broadcast where they are and what they are doing to anyone who cares to read it via social media."

In comparison, a small black box about the size of a cigarette packet that sits in their car and potentially reduces astronomical car insurance premiums might look like a small price to pay.

There are advantages, too. The technology includes tracking devices, so if your car is stolen it should help police recover it, in theory at least. These devices can also be of use if you are unfortunate enough to be involved in an accident, as the data they contain could be used to prove that you were not at fault, driving erratically or speeding. In fact, the US is currently debating whether to pass a law making it compulsory to have this technology – so cars, like airliners, would have a record of any accident they were involved in.

The trick to getting the cheapest car insurance

Getting the cheapest car insurance is, sadly, not as simple as just using a price comparison service. These websites - try Moneysupermarket's quote finder - provide an excellent starting point. But some major insurers only deal with customers direct so you will need to enter your details on their websites as well. These include Direct Line and Zurich.

Some insurers also offer special offers that are worth factoring in and are often not included on comparison websites. For instance, the Post Office will guarantee the over-50s that they will beat their renewal premium by £50 [click here].

All those taking car insurance with John Lewis before the end of October are entered into a draw to win a VW Golf Match, plus free insurance for a year.[find out more]